Incorrect calculations: sec(x) and csc(x) for large values of x

In this blog post, we explore incorrect calculations of the secant function sec(x) and cosecant function csc(x) for large numbers in MATLAB.

Example 1. Given that x = 1234567890888777.123, calculate sec(x) and csc(x).

Using MATLAB, I computed the values of sec(x) and csc(x) at x = 1234567890888777.123. The result is shown in the following screenshot.

From the above screenshot, it can be seen that the outputs from MATLAB are $-1.\red{059606794245841}$ and $-\red{3.024159505568874}$ respectively.

However, the correct values with 16 significant digits are -0.1116013690832344e1 and -0.2252452617594792e1, respectively (as provided by ISRealsoft).

Therefore, out of the 32 significant digits in the two outputs from MATLAB, only 1 digit is correct. The error rates are 15/16 = 93.75% and 16/16 = 100%, respectively.

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